A hybrid approach for coarse-graining helical peptoids: Solvation, secondary structure, and assembly

Protein mimics such as peptoids form self-assembled nanostructures whose shape and function are governed by the side chain chemistry and secondary structure. Experiments have shown that a peptoid sequence with a helical secondary structure assembles into microspheres that are stable under various conditions. The conformation and organization of the peptoids within the assemblies remains unknown and is elucidated in this study via a hybrid, bottom-up coarse-graining approach. The resultant coarse-grained (CG) model preserves the chemical and structural details that are critical for capturing the secondary structure of the peptoid. The CG model accurately captures the overall conformation and solvation of the peptoids in an aqueous solution. Furthermore, the model resolves the assembly of multiple peptoids into a hemispherical aggregate that is in qualitative agreement with the corresponding results from experiments. The mildly hydrophilic peptoid residues are placed along the curved interface of the aggregate. The composition of the residues on the exterior of the aggregate is determined by two conformations adopted by the peptoid chains. Hence, the CG model simultaneously captures sequence-specific features and the assembly of a large number of peptoids. This multiscale, multiresolution coarse-graining approach could help in predicting the organization and packing of other tunable oligomeric sequences of relevance to biomedicine and electronics.

Perspectives on weak interactions in complex materials at different length scales

Nanocomposite materials consist of nanometer-sized quantum objects such as atoms, molecules, voids or nanoparticles embedded in a host material. These quantum objects can be exploited as a super-structure, which can be designed to create material properties targeted for specific applications. For electromagnetism, such targeted properties include field enhancements around the bandgap of a semiconductor used for solar cells, directional decay in topological insulators, high kinetic inductance in superconducting circuits, and many more. Despite very different application areas, all of these properties are united by the common aim of exploiting collective interaction effects between quantum objects. The literature on the topic spreads over very many different disciplines and scientific communities. In this review, we present a cross-disciplinary overview of different approaches for the creation, analysis and theoretical description of nanocomposites with applications related to electromagnetic properties.

Coarse-Grained Model Incorporating Short- and Long-Range Effective Potentials for the Fast Simulation of Micelle Formation in Solutions of Ionic Surfactants

A coarse-grained model comprising short- and long-range effective potentials, parametrized with the iterative Boltzmann inversion (IBI) method, is presented for capturing micelle formation in aqueous solutions of ionic surfactants using as a model system sodium dodecyl sulfate (SDS). In the coarse-grained (CG) model, each SDS molecule is represented as a sequence of four beads while each water molecule is modeled as a single bead. The proposed CG scheme involves ten potential energy functions: four of them describe bonded interactions and control the distribution functions of intramolecular degrees of freedom (bond lengths, valence angles, and dihedrals) along an SDS molecule while the other six account for intermolecular interactions between pairs of SDS and water beads and control the radial distribution functions. The nonbonded effective potentials between coarse-grained SDS molecules extend up to about 12 nm and capture structural and morphological features of the micellar solution both at short and long distances. The long-range component of these potentials, in particular, captures correlations between surfactant molecules belonging to different micelles and is essential to describe ordering associated with micelle formation. A new strategy is introduced for determining the effective potentials through IBI by using information (target distribution functions) extracted from independent atomistic simulations of a micellar reference system (a salt-free SDS solution at total surfactant concentration c_T equal to 103 mM, temperature T equal to 300 K, and pressure P equal to 1 atm) obtained through a multiscale approach described in an earlier study. It employs several optimization steps for bonded and nonbonded interactions and a gradual parametrization of the short- and long-range components of the latter, followed by reparametrization of the bonded ones. The proposed CG model can reproduce remarkably accurately the microstructure and morphology of the reference system within only a few hours of computational time. It is therefore very promising for future studies of structural and morphological behavior of various liquid surfactant formulations.

Insights into the Phase Diagram of Pluronic L64 Using Coarse-Grained Molecular Dynamics Simulations

We investigate the concentration-dependent phase diagram of pluronic L64 in aqueous media at 300 and 320 K using coarse-grained (CG) molecular dynamics (MD) simulations. The CG model is derived by adapting the Martini model for nonbonded interactions along with the Boltzmann inversion (BI) of bonded interactions from all-atom (AA) simulations. Our derived CG model successfully captures the experimentally observed micellar-, hexagonal-, lamellar-, and polymer-rich solution phase. The end-to-end distance reveals the conformational change from an open-chain structure in the micellar phase to a folded-chain structure in the lamellar phase, increasing the orientational order. An increase in temperature leads to expulsion of water molecules from the L64 moiety, suggesting an increase in L64 hydrophobicity. Thermodynamic analysis using the two-phase thermodynamics (2PT) method suggests the entropy of the system decreases with increasing L64 concentration and the decrease in free energy (F) with temperature is mainly driven by the entropic factor (-TS). Further, the increase in aggregation number at lower concentrations and self-assembly at very high concentrations is energetically driven, whereas the change from the micellar phase to the lamellar phase with increasing L64 concentration is entropically driven. Our model provides molecular insights into L64 phases which can be further explored to design functionality-based suprastructures for drug delivery and tissue engineering applications.

A hybrid coarse-grained model for structure, solvation and assembly of lipid-like peptides

Reconstituted photosynthetic proteins which are activated upon exposure to solar energy hold enormous potential for powering future solid state devices and solar cells. The functionality and integration of these proteins into such devices has been successfully enabled by lipid-like peptides. Yet, a fundamental understanding of the organization of these peptides with respect to the photosynthetic proteins and themselves remains unknown and is critical for guiding the design of such light-activated devices. This study investigates the relative organization of one such peptide sequence V₆K₂ (V: valine and K: lysine) within assemblies. Given the expansive spatiotemporal scales associated with this study, a hybrid coarse-grained (CG) model which captures the structure, conformation and aggregation of the peptide is adopted. The CG model uses a combination of iterative Boltzmann inversion and force matching to provide insight into the relative organization of V₆K₂ in assemblies. The CG model reproduces the structure of a V₆K₂ peptide sequence along with its all atom (AA) solvation structure. The relative organization of multiple peptides in an assembly, as captured by CG simulations, is in agreement with corresponding results from AA simulations. Also, a backmapping procedure reintroduces the AA details of the peptides within the aggregates captured by the CG model to demonstrate the relative organization of the peptides. Furthermore, a large number of peptides self-assemble into an elongated micelle in the CG simulation, which is consistent with experimental findings. The coarse-graining procedure is tested for transferability to longer peptide sequences, and hence can be extended to other amphiphilic peptide sequences.

A program for automatically predicting supramolecular aggregates and its application to urea and porphin

Not only the molecular structure but also the presence or absence of aggregates determines many properties of organic materials. Theoretical investigation of such aggregates requires the prediction of a suitable set of diverse structures. Here, we present the open-source program EnergyScan for the unbiased prediction of geometrically diverse sets of small aggregates. Its bottom-up approach is complementary to existing ones by performing a detailed scan of an aggregate's potential energy surface, from which diverse local energy minima are selected. We crossvalidate this approach by predicting both literature-known and heretofore unreported geometries of the urea dimer. We also predict a diverse set of dimers of the less intensely studied case of porphin, which we investigate further using quantum chemistry. For several dimers, we find strong deviations from a reference absorption spectrum, which we explain using computed transition densities. This proof of principle clearly shows that EnergyScan successfully predicts aggregates exhibiting large structural and spectral diversity. © 2018 Wiley Periodicals, Inc.

Coarse-Grained Molecular Dynamics Force-Field for Polyacrylamide in Infinite Dilution Derived from Iterative Boltzmann Inversion and MARTINI Force-Field

We present a mesoscale model of aqueous polyacrylamide in the infinitely dilute concentration regime, by combining an extant coarse-grained (CG) force-field, MARTINI, and the Iterative Boltzmann Inversion protocol (IBI). MARTINI force-field was used to retain the thermodynamics of solvation of the polymer in water, whereas the structural properties and intrapolymer interactions were optimized by IBI. Atomistic molecular dynamics simulations of polymer in water were performed to benchmark the mesoscale simulations. Our results from the CG model show excellent agreement in structure with the atomistic system. We also studied the dynamical behavior of our CG system by computing the shear viscosity and compared it with the standard IBI model. The viscosity trends of our model were similar to the atomistic system, whereas the standard IBI model was highly dissimilar as expected. In summary, our hybrid CG model sufficiently mimics an infinitely dilute system, and is superior to both MARTINI and IBI in representing the structure and thermodynamics of the atomistic system, respectively. Our hybrid coarse-graining strategy promises applicability in large-scale simulations of polymeric/biological systems where the structure needs to be replicated accurately while preserving the thermodynamics of a smoother surrounding.

Rapid Sampling of Folding Equilibria of β-Peptides in Methanol Using a Supramolecular Solvent Model

Molecular dynamics simulation of biomolecules in solvent using an atomic model for both the biomolecules and the solvent molecules is still computationally rather demanding considering the time scale of the biomolecular motions. The use of a supramolecular coarse-grained (CG) model can speed up the simulation considerably, but it also reduces the accuracy inevitably. Combining an atomic fine-grained (FG) level of modeling for the biomolecules and a supramolecular CG level for the solvent into a hybrid system, the increased computational efficiency may outweigh the loss of accuracy with respect to the biomolecular properties in the hybrid FG/CG simulation. Here, a previously published CG methanol model is reparametrized, and then a 1:1 mixture of FG and CG methanol is used to calibrate the FG-CG interactions using thermodynamic and dielectric screening data for liquid methanol. The FG-CG interaction parameter set is applied in hybrid FG/CG solute/solvent simulations of the folding equilibria of three β-peptides that adopt different folds. The properties of the peptides are compared with those obtained in FG solvent simulations and with experimental NMR data. The comparison shows that the folding equilibria in the pure CG solvent simulations are different from those in the FG solvent simulations because of the lack of hydrogen-bonding partners in the supramolecular CG solvent. Next, we introduced an FG methanol layer around the peptides in CG solvent to recover the hydrogen-bonding pattern of the FG solvent simulations. The result shows that with the FG methanol layer, the folding equilibria of the three β-peptides are very similar to those in the FG solvent simulations, while the computational efficiency is at least 3 times higher and the cutoff radius for nonbonded interactions could be increased from 1.4 to 2.0 nm.

Derivation of coarse-grained simulation models of chlorophyll molecules in lipid bilayers for applications in light harvesting systems

The correct interplay of interactions between protein, pigment and lipid molecules is highly relevant for our understanding of the association behavior of the light harvesting complex (LHCII) of green plants. To cover the relevant time and length scales in this multicomponent system, a multi-scale simulation ansatz is employed that subsequently uses a classical all atomistic (AA) model to derive a suitable coarse grained (CG) model which can be backmapped into the AA resolution, aiming for a seamless conversion between two scales. Such an approach requires a faithful description of not only the protein and lipid components, but also the interaction functions for the indispensable pigment molecules, chlorophyll b and chlorophyll a (referred to as chl b/chl a). In this paper we develop a CG model for chl b and chl a in a dipalmitoylphosphatidyl choline (DPPC) bilayer system. The structural properties and the distribution behavior of chl within the lipid bilayer in the CG simulations are consistent with those of AA reference simulations. The non-bonded potentials are parameterized such that they fit to the thermodynamics based MARTINI force-field for the lipid bilayer and the protein. The CG simulation shows chl aggregation in the lipid bilayer which is supported by fluorescence quenching experiments. It is shown that the derived chl model is well suited for CG simulations of stable, structurally consistent, trimeric LHCII and can in the future be used to study their large scale aggregation behavior.

Relative Entropy and Optimization-Driven Coarse-Graining Methods in VOTCA

We discuss recent advances of the VOTCA package for systematic coarse-graining. Two methods have been implemented, namely the downhill simplex optimization and the relative entropy minimization. We illustrate the new methods by coarse-graining SPC/E bulk water and more complex water-methanol mixture systems. The CG potentials obtained from both methods are then evaluated by comparing the pair distributions from the coarse-grained to the reference atomistic simulations. In addition to the newly implemented methods, we have also added a parallel analysis framework to improve the computational efficiency of the coarse-graining process.

Investigation of coarse-grained mappings via an iterative generalized Yvon-Born-Green method

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

Coarse-Grained Models for Protein-Cell Membrane Interactions

The physiological properties of biological soft matter are the product of collective interactions, which span many time and length scales. Recent computational modeling efforts have helped illuminate experiments that characterize the ways in which proteins modulate membrane physics. Linking these models across time and length scales in a multiscale model explains how atomistic information propagates to larger scales. This paper reviews continuum modeling and coarse-grained molecular dynamics methods, which connect atomistic simulations and single-molecule experiments with the observed microscopic or mesoscale properties of soft-matter systems essential to our understanding of cells, particularly those involved in sculpting and remodeling cell membranes.